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CCSS Math: 4.NF.A.1

So I've got a whole
pizza here, and let's say that I were to cut it
into two equal pieces. Let me cut it right over
here into 2 equal pieces. And let's say that I ate
one of those 2 equal pieces. So let's say I ate all
of this right over here. What fraction of the
pizza have I eaten? Well, I took the
whole and I divide it into two equal pieces, and
then I ate one of those pieces. So I ate 1/2 of the pizza. Now, let's imagine that instead
of cutting that pizza into only 2 equal pieces,
let's imagine instead that decide to cut it
into 4 equal pieces. So let's draw that. So 4 equal pieces. So I could cut once
this way and then I could cut it once this way. And so here I have
4 equal pieces. But let's say that I want to
eat the same amount of pizza. How many of these 4 equal
pieces would I have to eat. I encourage you to pause the
video and think about that. Well, I would eat this piece. You could imagine me eating
this piece and this piece right over here. I've eaten the same
amount of the pizza. Each of these pieces you could
imagine got cut into 2 pieces when I cut the whole
pizza this way. And so now I have to
eat 2 slices of the 4, as opposed to 1 slice of the 2. So I just ate 2 out
of the 4 slices. I'm using different
numbers here. Here I'm using a
1 in the numerator and 2 in the denominator. Here, I'm using a
2 in the numerator and a 4 in the denominator. These two fractions
represent the same quantity. I ate the same amount of pizza. If I eat 2/4 of a pizza, if I
eat 2 out of 4 equal pieces, that's the same
fraction of the pizza as if I eat 1 out
of 2 equal pieces. So we would say that
these two things are equivalent fractions. Now let's do another
one like this. Instead of just dividing
it into 4 equal pieces, let's divide it
into 8 equal pieces. So now we could
cut once like this. So now we have 2 equal pieces. Cut once like this. Now we have 4 equal pieces. And then divide each of
those 4 pieces into 2 pieces. So I'll cut those
in-- So let's see. I want to make
them equal pieces. Those don't look as
equal as I would like. So that looks more equal, and
that looks reasonably equal. So now how many equal
pieces do I have? I have 8 equal pieces. But let's say I wanted to eat
the same fraction of the pizza. So I could eat all of these
pieces right over here. Well, how many of those 8
equal pieces have I eaten? Well, I've eaten 1, 2, 3,
4 of those 8 equal pieces. And so once again, this
fraction, 4 of 8, or 4/8, is equivalent to 2/4,
which is equivalent to 1/2. And you might see a little
bit of a pattern here. Going from this scenario
to this scenario, I got twice as
many equal slices. Because I had twice
as many equal slices, I needed to eat two times
the number of slices. So I multiply the
denominator by 2, and I multiply the
numerator by 2. If I multiply the numerator
and the denominator by the same number,
then I'm not changing what that fraction represents. And you see that over here. Going from 4 slices to 8
slices, I cut every slice, I turned every slice
into 2 more slices, so I had twice as many slices. And then if I want to
eat the same amount, I have to eat twice
as many pieces. So all of these, 1/2, 2/4, four
4/8, and I could keep going. I could do 8/16. I could do 16/32. All of these would be
equivalent fractions.